Abstract: Let be a connected reductive algebraic group defined over a field of characteristic not 2, an involution of defined over , a -open subgroup of the fixed point group of , (resp. ) the set of -rational points of (resp. ) and the corresponding symmetric -variety. A representation induced from a parabolic -subgroup of generically contributes to the Plancherel decomposition of if and only if the parabolic -subgroup is -split. So for a study of these induced representations a detailed description of the -conjucagy classes of these -split parabolic -subgroups is needed.

In this paper we give a description of these conjugacy classes for general symmetric -varieties. This description can be refined to give a more detailed description in a number of cases. These results are of importance for studying representations for real and -adic symmetric -varieties.